1,1,147,109,0.559000," ","int(sin(f*x+e)^3*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{-a^{2} c \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{a^{2} c \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+a^{2} c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-a^2*c*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/5*a^2*c*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^2*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/3*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
2,1,126,86,0.459000," ","int(sin(f*x+e)^2*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{\frac{a^{2} c \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-a^{2} c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(1/5*a^2*c*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-a^2*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/3*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
3,1,106,69,0.378000," ","int(sin(f*x+e)*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{-a^{2} c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a^{2} c \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-a^2*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/3*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2*c*cos(f*x+e))","A"
4,1,78,46,0.275000," ","int((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{\frac{a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-a^{2} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a^{2} c \cos \left(f x +e \right)+a^{2} c \left(f x +e \right)}{f}"," ",0,"1/f*(1/3*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e)-a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2*c*cos(f*x+e)+a^2*c*(f*x+e))","A"
5,1,78,59,0.188000," ","int(csc(f*x+e)*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{a^{2} c \cos \left(f x +e \right) \sin \left(f x +e \right)}{2 f}+\frac{a^{2} c x}{2}+\frac{a^{2} c e}{2 f}+\frac{a^{2} c \cos \left(f x +e \right)}{f}+\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"1/2*a^2*c*cos(f*x+e)*sin(f*x+e)/f+1/2*a^2*c*x+1/2/f*a^2*c*e+a^2*c*cos(f*x+e)/f+1/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))","A"
6,1,72,53,0.280000," ","int(csc(f*x+e)^2*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","-a^{2} c x +\frac{a^{2} c \cos \left(f x +e \right)}{f}-\frac{a^{2} c \cot \left(f x +e \right)}{f}+\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}-\frac{a^{2} c e}{f}"," ",0,"-a^2*c*x+a^2*c*cos(f*x+e)/f-a^2*c*cot(f*x+e)/f+1/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))-1/f*a^2*c*e","A"
7,1,80,60,0.448000," ","int(csc(f*x+e)^3*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","-a^{2} c x -\frac{a^{2} c e}{f}-\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}-\frac{a^{2} c \cot \left(f x +e \right)}{f}-\frac{a^{2} c \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}"," ",0,"-a^2*c*x-1/f*a^2*c*e-1/2/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))-a^2*c*cot(f*x+e)/f-1/2*a^2*c*cot(f*x+e)*csc(f*x+e)/f","A"
8,1,86,55,0.504000," ","int(csc(f*x+e)^4*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","-\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}+\frac{a^{2} c \cot \left(f x +e \right)}{3 f}-\frac{a^{2} c \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{3 f}"," ",0,"-1/2/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))+1/3*a^2*c*cot(f*x+e)/f-1/2*a^2*c*cot(f*x+e)*csc(f*x+e)/f-1/3/f*a^2*c*cot(f*x+e)*csc(f*x+e)^2","A"
9,1,109,78,0.594000," ","int(csc(f*x+e)^5*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{a^{2} c \cot \left(f x +e \right)}{3 f}+\frac{a^{2} c \cot \left(f x +e \right) \csc \left(f x +e \right)}{8 f}-\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{3 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{4 f}"," ",0,"1/3*a^2*c*cot(f*x+e)/f+1/8*a^2*c*cot(f*x+e)*csc(f*x+e)/f-1/8/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))-1/3/f*a^2*c*cot(f*x+e)*csc(f*x+e)^2-1/4*a^2*c*cot(f*x+e)*csc(f*x+e)^3/f","A"
10,1,132,95,0.604000," ","int(csc(f*x+e)^6*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{a^{2} c \cot \left(f x +e \right) \csc \left(f x +e \right)}{8 f}-\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 f}+\frac{2 a^{2} c \cot \left(f x +e \right)}{15 f}+\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{15 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{4 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{4}\left(f x +e \right)\right)}{5 f}"," ",0,"1/8*a^2*c*cot(f*x+e)*csc(f*x+e)/f-1/8/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))+2/15*a^2*c*cot(f*x+e)/f+1/15/f*a^2*c*cot(f*x+e)*csc(f*x+e)^2-1/4*a^2*c*cot(f*x+e)*csc(f*x+e)^3/f-1/5/f*a^2*c*cot(f*x+e)*csc(f*x+e)^4","A"
11,1,155,118,0.631000," ","int(csc(f*x+e)^7*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{2 a^{2} c \cot \left(f x +e \right)}{15 f}+\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{15 f}+\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{24 f}+\frac{a^{2} c \cot \left(f x +e \right) \csc \left(f x +e \right)}{16 f}-\frac{a^{2} c \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{16 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{4}\left(f x +e \right)\right)}{5 f}-\frac{a^{2} c \cot \left(f x +e \right) \left(\csc^{5}\left(f x +e \right)\right)}{6 f}"," ",0,"2/15*a^2*c*cot(f*x+e)/f+1/15/f*a^2*c*cot(f*x+e)*csc(f*x+e)^2+1/24*a^2*c*cot(f*x+e)*csc(f*x+e)^3/f+1/16*a^2*c*cot(f*x+e)*csc(f*x+e)/f-1/16/f*a^2*c*ln(csc(f*x+e)-cot(f*x+e))-1/5/f*a^2*c*cot(f*x+e)*csc(f*x+e)^4-1/6*a^2*c*cot(f*x+e)*csc(f*x+e)^5/f","A"
12,1,78,112,1.073000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2)*(c-c*sin(d*x+c)),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{2} c \left(7 \left(\sin^{3}\left(d x +c \right)\right)+15 \left(\sin^{2}\left(d x +c \right)\right)+12 \sin \left(d x +c \right)+8\right)}{63 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/63*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^2*c*(7*sin(d*x+c)^3+15*sin(d*x+c)^2+12*sin(d*x+c)+8)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
13,1,79,61,1.374000," ","int((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c-c*sin(f*x+e)),x)","-\frac{2 \left(1+\sin \left(f x +e \right)\right) \left(\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a \sqrt{a -a \sin \left(f x +e \right)}-a^{\frac{3}{2}}\right)}{\sqrt{a}\, c \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-2/a^(1/2)/c*(1+sin(f*x+e))*(arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a*(a-a*sin(f*x+e))^(1/2)-a^(3/2))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
14,1,124,104,1.434000," ","int(1/sin(f*x+e)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \left(2 a^{\frac{5}{2}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \sqrt{a -a \sin \left(f x +e \right)}-4 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a^{2} \sqrt{a -a \sin \left(f x +e \right)}\right)}{2 c \,a^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/2*(1+sin(f*x+e))*(2*a^(5/2)+2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*(a-a*sin(f*x+e))^(1/2)-4*arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a^2*(a-a*sin(f*x+e))^(1/2))/c/a^(5/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
15,1,914,87,0.937000," ","int((g*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e)),x)","\frac{\left(4 \sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}\right) \sin \left(f x +e \right)-4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}+1\right) \sin \left(f x +e \right)-4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}-1\right) \sin \left(f x +e \right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}\right) \cos \left(f x +e \right)-4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}+1\right) \cos \left(f x +e \right)-4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}-1\right) \cos \left(f x +e \right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}\right) \cos \left(f x +e \right)+\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}\right)+4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}+1\right)+4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}-1\right)+\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}\right)\right) \sqrt{g \sin \left(f x +e \right)}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{4 c f \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}}"," ",0,"1/4/c/f*(4*2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1))*sin(f*x+e)-4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)+1)*sin(f*x+e)-4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)-1)*sin(f*x+e)-ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1))*sin(f*x+e)-ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1))*cos(f*x+e)-4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)+1)*cos(f*x+e)-4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)-1)*cos(f*x+e)-ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1))*cos(f*x+e)+ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1))+4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)+1)+4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)-1)+ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)))*(g*sin(f*x+e))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)/cos(f*x+e)/(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)","B"
16,1,45,39,0.650000," ","int((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x)","\frac{2 \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right)}{c f \sqrt{g \sin \left(f x +e \right)}\, \cos \left(f x +e \right)}"," ",0,"2/c/f*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)/(g*sin(f*x+e))^(1/2)/cos(f*x+e)","A"
17,1,190,96,0.783000," ","int((g*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","\frac{\sqrt{g \sin \left(f x +e \right)}\, \left(-1+\cos \left(f x +e \right)\right) \left(2 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\right) \cos \left(f x +e \right)-\cos \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}-\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\right)}{c f \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/c/f*(g*sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(2*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2))*cos(f*x+e)-cos(f*x+e)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)-(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2))/sin(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))","A"
18,1,117,99,0.645000," ","int(1/(c-c*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \sin \left(f x +e \right)}{c f \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sqrt{g \sin \left(f x +e \right)}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"1/c/f*(2*cos(f*x+e)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2))+sin(f*x+e)-cos(f*x+e)+1)*sin(f*x+e)/(-1+cos(f*x+e)+sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a*(1+sin(f*x+e)))^(1/2)","A"
19,1,74,42,0.655000," ","int((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2)/sin(f*x+e),x)","-\frac{\left(\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{f \cos \left(f x +e \right)}"," ",0,"-1/f*(ln(2/(cos(f*x+e)+1))-ln(-(-1+cos(f*x+e))/sin(f*x+e)))*(-c*(sin(f*x+e)-1))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)","A"
20,1,111,94,0.467000," ","int((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right)}{f \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/f*(a*(1+sin(f*x+e)))^(1/2)*(-1+cos(f*x+e)+sin(f*x+e))*(2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e))/sin(f*x+e)))/(-1+cos(f*x+e)-sin(f*x+e))/(-c*(sin(f*x+e)-1))^(1/2)","A"
21,1,112,92,0.483000," ","int((c-c*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(\ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"-1/f*(-1+cos(f*x+e)-sin(f*x+e))*(-c*(sin(f*x+e)-1))^(1/2)*(ln(-(-1+cos(f*x+e))/sin(f*x+e))-2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))/(a*(1+sin(f*x+e)))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))","A"
22,1,111,42,0.442000," ","int(1/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \cos \left(f x +e \right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-1/f*(ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e))/sin(f*x+e))+ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(1/2)","B"
23,1,120,85,1.465000," ","int((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(d \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}}-\arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) a \sqrt{a \left(c +d \right) d}\right)}{\sqrt{a}\, c \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/a^(1/2)*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(d*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)-arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*a*(a*(c+d)*d)^(1/2))/c/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
24,1,208,136,1.931000," ","int(1/sin(f*x+e)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(2 d^{2} \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}}-\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c \,a^{2} \sqrt{a \left(c +d \right) d}+2 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a^{2} \sqrt{a \left(c +d \right) d}\, c -2 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a^{2} \sqrt{a \left(c +d \right) d}\, d \right)}{c \,a^{\frac{5}{2}} \left(c -d \right) \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(2*d^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)-2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c*a^2*(a*(c+d)*d)^(1/2)+2*arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a^2*(a*(c+d)*d)^(1/2)*c-2*arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a^2*(a*(c+d)*d)^(1/2)*d)/c/a^(5/2)/(c-d)/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
25,1,1025,117,0.948000," ","int((g*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x)","\frac{\sqrt{g \sin \left(f x +e \right)}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)\right) \left(2 \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{2}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, c +2 \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{2}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, c^{2}-2 \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{2}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, c d -2 \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{2}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, c +2 \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{2}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, c^{2}-2 \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{2}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, c d +\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}+4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}+1\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}+4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}-1\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}+\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\right) \sqrt{2}}{2 f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, d \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}"," ",0,"1/2/f*(g*sin(f*x+e))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)*(-1+cos(f*x+e))*(2*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*(-(c-d)*(c+d))^(1/2)*2^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*c+2*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*2^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*c^2-2*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*2^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*c*d-2*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*(-(c-d)*(c+d))^(1/2)*2^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*c+2*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*2^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*c^2-2*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*2^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*c*d+ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1))*(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)+4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)+1)*(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)+4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)-1)*(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)+ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1))*(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))/sin(f*x+e)/(-1+cos(f*x+e)-sin(f*x+e))/(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)/d/(-(c-d)*(c+d))^(1/2)/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)","B"
26,1,526,63,0.557000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x)","\frac{2 \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{-\left(c -d \right) \left(c +d \right)}+\arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, c -\arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, d -\arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, \sqrt{-\left(c -d \right) \left(c +d \right)}+\arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, c -\arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, d \right)}{f \sqrt{g \sin \left(f x +e \right)}\, \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}"," ",0,"2/f*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*(-(c-d)*(c+d))^(1/2)+arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*c-arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*d-arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*(-(c-d)*(c+d))^(1/2)+arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*c-arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*d)/(g*sin(f*x+e))^(1/2)/(-1+cos(f*x+e)-sin(f*x+e))/(-(c-d)*(c+d))^(1/2)/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)","B"
27,1,614,131,0.751000," ","int((g*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{g \sin \left(f x +e \right)}\, \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(2 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}+\sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) c -\sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) c +\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) c^{2}-\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) c d +\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) c^{2}-\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) c d \right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(c -d \right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}"," ",0,"-1/f*(g*sin(f*x+e))^(1/2)*(1-cos(f*x+e)+sin(f*x+e))*(2*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2))*(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)+(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*c-(-(c-d)*(c+d))^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*c+(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*c^2-(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*c*d+((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*c^2-((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*c*d)/(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)/(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)/(c-d)/(-(c-d)*(c+d))^(1/2)/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)","B"
28,1,621,133,0.557000," ","int(1/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sin \left(f x +e \right) \left(2 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}+\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, d +\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) c d -\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \arctanh \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}\right) d^{2}-\arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, \sqrt{-\left(c -d \right) \left(c +d \right)}\, d +\sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, \arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) c d -\arctan \left(\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, c}{\sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}}\right) \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}\, d^{2}\right)}{f \sqrt{g \sin \left(f x +e \right)}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)\right) \left(c -d \right) \sqrt{-\left(c -d \right) \left(c +d \right)}\, \sqrt{\left(\sqrt{-\left(c -d \right) \left(c +d \right)}+d \right) c}\, \sqrt{\left(-d +\sqrt{-\left(c -d \right) \left(c +d \right)}\right) c}}"," ",0,"1/f*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-1+cos(f*x+e)-sin(f*x+e))*sin(f*x+e)*(2*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2))*(-(c-d)*(c+d))^(1/2)*(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)+(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*(-(c-d)*(c+d))^(1/2)*d+(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*c*d-(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)*arctanh((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2))*d^2-arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*(-(c-d)*(c+d))^(1/2)*d+((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*c*d-arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*c/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2))*((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)*d^2)/(g*sin(f*x+e))^(1/2)/(a*(1+sin(f*x+e)))^(1/2)/(-1+cos(f*x+e))/(c-d)/(-(c-d)*(c+d))^(1/2)/(((-(c-d)*(c+d))^(1/2)+d)*c)^(1/2)/((-d+(-(c-d)*(c+d))^(1/2))*c)^(1/2)","B"
29,1,593,323,4.934000," ","int((a+b*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+c*sin(f*x+e)),x)","\frac{\sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{2 \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, b \EllipticPi \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, -\frac{\left(-\frac{a}{b}+1\right) b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{\sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\left(-a +b \right) \left(-\frac{-b \left(\sin^{2}\left(f x +e \right)\right)-a \sin \left(f x +e \right)+b \sin \left(f x +e \right)+a}{\left(a -b \right) \sqrt{\left(-b \sin \left(f x +e \right)-a \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(2 a -2 b \right) \sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\left(a -b \right) \sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{c \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)/c*(-2*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*b*EllipticPi(((a+b*sin(f*x+e))/(a-b))^(1/2),-(-a/b+1)/a*b,((a-b)/(a+b))^(1/2))+(-a+b)*(-(-b*sin(f*x+e)^2-a*sin(f*x+e)+b*sin(f*x+e)+a)/(a-b)/((-b*sin(f*x+e)-a)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*b/(2*a-2*b)*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-b/(a-b)*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))))/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
30,1,587,331,4.918000," ","int(1/sin(f*x+e)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{2 \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, b \EllipticPi \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, -\frac{\left(-\frac{a}{b}+1\right) b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{\sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a}+\frac{-b \left(\sin^{2}\left(f x +e \right)\right)-a \sin \left(f x +e \right)+b \sin \left(f x +e \right)+a}{\left(a -b \right) \sqrt{\left(-b \sin \left(f x +e \right)-a \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(2 a -2 b \right) \sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\left(a -b \right) \sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{c \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)/c*(-2*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)/a*b*EllipticPi(((a+b*sin(f*x+e))/(a-b))^(1/2),-(-a/b+1)/a*b,((a-b)/(a+b))^(1/2))+(-b*sin(f*x+e)^2-a*sin(f*x+e)+b*sin(f*x+e)+a)/(a-b)/((-b*sin(f*x+e)-a)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*b/(2*a-2*b)*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+b/(a-b)*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
31,1,22962,243,1.392000," ","int((g*sin(f*x+e))^(1/2)*(a+b*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
32,1,6804,108,0.707000," ","int((a+b*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
33,1,6817,232,0.912000," ","int((g*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
34,1,9043,236,0.737000," ","int(1/(c+c*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
35,1,4546,99,0.829000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e),x)","\text{output too large to display}"," ",0,"-1/f*(arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*d*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c^(1/2)-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(7/2)*d*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)*sin(f*x+e)+2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(5/2)*d^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)*cos(f*x+e)+2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(5/2)*d^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)*sin(f*x+e)-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(3/2)*d^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)*cos(f*x+e)-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(3/2)*d^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)*sin(f*x+e)+arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*c^(3/2)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(d^2/c^2)^(1/2)-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(7/2)*d*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)*cos(f*x+e)-2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(5/2)*d^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(5/2)*d^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*cos(f*x+e)+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(5/2)*d^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*sin(f*x+e)+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^4*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*c^(1/2)*sin(f*x+e)-2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(3/2)*d^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*sin(f*x+e)+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^4*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*c^(1/2)*cos(f*x+e)-2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(3/2)*d^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*cos(f*x+e)+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(3/2)*d^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(5/2)*d^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)+2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(3/2)*d^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^4*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*c^(1/2)+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^(7/2)*d*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(d^2/c^2)^(1/2)+ln((c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*sin(f*x+e)+c)/sin(f*x+e)/c^(1/2))*c^3*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*sin(f*x+e)-2*ln((c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*sin(f*x+e)+c)/sin(f*x+e)/c^(1/2))*c^2*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*sin(f*x+e)+ln((c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*sin(f*x+e)+c)/sin(f*x+e)/c^(1/2))*c*d^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*sin(f*x+e)-ln(-2*(c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-d*cos(f*x+e)+c*sin(f*x+e)+d)/(-1+cos(f*x+e)))*c^3*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*sin(f*x+e)+2*ln(-2*(c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-d*cos(f*x+e)+c*sin(f*x+e)+d)/(-1+cos(f*x+e)))*c^2*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*sin(f*x+e)-ln(-2*(c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-d*cos(f*x+e)+c*sin(f*x+e)+d)/(-1+cos(f*x+e)))*c*d^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*sin(f*x+e)-arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*c^(3/2)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(d^2/c^2)^(1/2)*cos(f*x+e)+arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*c^(3/2)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(d^2/c^2)^(1/2)*sin(f*x+e)-arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*d*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c^(1/2)*cos(f*x+e)+arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*d*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c^(1/2)*sin(f*x+e))*(a*(1+sin(f*x+e)))^(1/2)*(c+d*sin(f*x+e))^(1/2)/(cos(f*x+e)^2*d+d*sin(f*x+e)*cos(f*x+e)+c*cos(f*x+e)-c*sin(f*x+e)-d*sin(f*x+e)-c-d)/d/(c^2-2*c*d+d^2)/(-(d^2/c^2)^(1/2)*c)^(1/2)/c^(1/2)","B"
36,1,231,49,0.541000," ","int((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, \sqrt{2}\, \left(\ln \left(\frac{\sqrt{c}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\sin \left(f x +e \right) \sqrt{c}}\right)-\ln \left(-\frac{2 \left(\sqrt{c}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-d \cos \left(f x +e \right)+c \sin \left(f x +e \right)+d \right)}{-1+\cos \left(f x +e \right)}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{f \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{c}}"," ",0,"1/f*(a*(1+sin(f*x+e)))^(1/2)*(c+d*sin(f*x+e))^(1/2)*2^(1/2)*(ln((c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*sin(f*x+e)+c)/sin(f*x+e)/c^(1/2))-ln(-2*(c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-d*cos(f*x+e)+c*sin(f*x+e)+d)/(-1+cos(f*x+e))))*(-1+cos(f*x+e))/sin(f*x+e)/(-1+cos(f*x+e)-sin(f*x+e))/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/c^(1/2)","B"
37,1,340,113,0.519000," ","int((c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{c +d \sin \left(f x +e \right)}\, \left(-c \ln \left(-\frac{2 \left(\sqrt{c}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-d \cos \left(f x +e \right)+c \sin \left(f x +e \right)+d \right)}{-1+\cos \left(f x +e \right)}\right)+\sqrt{2 c -2 d}\, \ln \left(-\frac{2 \left(\sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+c \sin \left(f x +e \right)-d \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d \right)}{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}\right) \sqrt{c}+\ln \left(\frac{\sqrt{c}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\sin \left(f x +e \right) \sqrt{c}}\right) c \right) \sqrt{2}}{2 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{c}}"," ",0,"-1/2/f*(-1+cos(f*x+e)-sin(f*x+e))*(c+d*sin(f*x+e))^(1/2)*(-c*ln(-2*(c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-d*cos(f*x+e)+c*sin(f*x+e)+d)/(-1+cos(f*x+e)))+(2*c-2*d)^(1/2)*ln(-2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(-1+cos(f*x+e)-sin(f*x+e)))*c^(1/2)+ln((c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*sin(f*x+e)+c)/sin(f*x+e)/c^(1/2))*c)/(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)*2^(1/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/c^(1/2)","B"
38,1,357,113,0.405000," ","int(1/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \sqrt{c +d \sin \left(f x +e \right)}\, \left(\ln \left(\frac{\sqrt{c}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-c \cos \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\sin \left(f x +e \right) \sqrt{c}}\right) \sqrt{2 c -2 d}+2 \ln \left(-\frac{2 \left(\sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+c \sin \left(f x +e \right)-d \sin \left(f x +e \right)+c \cos \left(f x +e \right)-d \cos \left(f x +e \right)-c +d \right)}{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}\right) \sqrt{c}-\ln \left(-\frac{2 \left(\sqrt{c}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-d \cos \left(f x +e \right)+c \sin \left(f x +e \right)+d \right)}{-1+\cos \left(f x +e \right)}\right) \sqrt{2 c -2 d}\right) \sqrt{2}}{2 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{c}\, \sqrt{2 c -2 d}}"," ",0,"-1/2/f*(-1+cos(f*x+e)-sin(f*x+e))*(c+d*sin(f*x+e))^(1/2)*(ln((c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-c*cos(f*x+e)+d*sin(f*x+e)+c)/sin(f*x+e)/c^(1/2))*(2*c-2*d)^(1/2)+2*ln(-2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(-1+cos(f*x+e)-sin(f*x+e)))*c^(1/2)-ln(-2*(c^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-d*cos(f*x+e)+c*sin(f*x+e)+d)/(-1+cos(f*x+e)))*(2*c-2*d)^(1/2))/(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)*2^(1/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/c^(1/2)/(2*c-2*d)^(1/2)","B"
39,1,606,171,0.553000," ","int(sin(f*x+e)^2/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),x)","\frac{8 c^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right)}{f \left(4 a^{2} d^{2}-8 a b c d +4 b^{2} c^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2} b \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{2 a \,b^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} d}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{2 a^{2} c b}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{2 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b d}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2} c}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"8/f*c^2/(4*a^2*d^2-8*a*b*c*d+4*b^2*c^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))-2/f*a^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)*b/(a^2-b^2)*tan(1/2*f*x+1/2*e)*d+2/f*a/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)*b^2/(a^2-b^2)*tan(1/2*f*x+1/2*e)*c-2/f*a^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/(a^2-b^2)*d+2/f*a^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/(a^2-b^2)*c*b-2/f*a^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c-2/f*a^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*b*d+4/f*a/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*b^2*c","B"
40,1,190,212,2.066000," ","int((c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+b*sin(f*x+e)),x)","\frac{2 \left(\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, -\frac{\left(c -d \right) b}{d a -c b}, \sqrt{\frac{c -d}{c +d}}\right)-\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{c -d}{c}, \sqrt{\frac{c -d}{c +d}}\right)\right) \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \left(c -d \right)}{a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2*(EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),-(c-d)*b/(a*d-b*c),((c-d)/(c+d))^(1/2))-EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(c-d)/c,((c-d)/(c+d))^(1/2)))*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(c-d)/a/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
41,1,254,204,1.901000," ","int(1/sin(f*x+e)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","-\frac{2 \left(c -d \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \left(b \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, -\frac{\left(c -d \right) b}{d a -c b}, \sqrt{\frac{c -d}{c +d}}\right) c +\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{c -d}{c}, \sqrt{\frac{c -d}{c +d}}\right) a d -\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{c -d}{c}, \sqrt{\frac{c -d}{c +d}}\right) b c \right)}{a \left(d a -c b \right) c \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2*(c-d)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*(b*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),-(c-d)*b/(a*d-b*c),((c-d)/(c+d))^(1/2))*c+EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(c-d)/c,((c-d)/(c+d))^(1/2))*a*d-EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(c-d)/c,((c-d)/(c+d))^(1/2))*b*c)/a/(a*d-b*c)/c/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
42,1,6196,235,0.842000," ","int((g*sin(f*x+e))^(1/2)*(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
43,1,3291,231,0.591000," ","int((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-1/f*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(a*d-b*c)*(2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)*b-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a*c+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*b*d-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*a^2+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*b^2-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*d-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*c+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2*d+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)*b+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a*c-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*b*d-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*a^2+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*b^2+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*d+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*c-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2*d-4*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)*b+2*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*a^2-4*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*b^2)*sin(f*x+e)^2*2^(1/2)/(a+b*sin(f*x+e))^(1/2)/(g*sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/(-c^2+d^2)^(1/2)/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b)/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b)","B"
44,1,2924,107,0.827000," ","int((g*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/f*(EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*d-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*a^2+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*c+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a*c-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2*d+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*b^2-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*b*d+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)*b-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*d-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*a^2-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*c-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a*c+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2*d+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-c^2+d^2)^(1/2)*b^2+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*b*d+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)*b)*(g*sin(f*x+e))^(1/2)*sin(f*x+e)/(a+b*sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*2^(1/2)/(-1+cos(f*x+e))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b)/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b)/(-c^2+d^2)^(1/2)","B"
45,1,3690,227,0.595000," ","int(1/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-1/f/(a+b*sin(f*x+e))^(1/2)*(4*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*d*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)-4*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2*c*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)-2*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*d*(-c^2+d^2)^(1/2)+2*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b*c*(-c^2+d^2)^(1/2)+4*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^2*d*(-c^2+d^2)^(1/2)-4*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^3*c*(-c^2+d^2)^(1/2)-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*d*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*d*(-c^2+d^2)^(1/2)-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^2*d*(-c^2+d^2)^(1/2)-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*d*(-a^2+b^2)^(1/2)*(-c^2+d^2)^(1/2)+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*d*(-c^2+d^2)^(1/2)-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^2*d*(-c^2+d^2)^(1/2)-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*c*d*(-a^2+b^2)^(1/2)+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*d^2*(-a^2+b^2)^(1/2)-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*d^2-EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b*c*d+2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^2*d^2+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*c*d*(-a^2+b^2)^(1/2)-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b*d^2*(-a^2+b^2)^(1/2)+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*d^2+EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b*c*d-2*EllipticPi((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),(b+(-a^2+b^2)^(1/2))*c/(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^2*d^2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*sin(f*x+e)^2*2^(1/2)/(g*sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b)/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b)/(-c^2+d^2)^(1/2)","B"
46,1,6052,235,0.993000," ","int((c+d*sin(f*x+e))^(1/2)*(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
47,1,2856,107,0.853000," ","int((g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/f*(EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*a*c*d+EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*a*c*(-c^2+d^2)^(1/2)+EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*b*c^2-2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*b*d^2-2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*b*d*(-c^2+d^2)^(1/2)-EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*c^2*(-a^2+b^2)^(1/2)+2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*d^2*(-a^2+b^2)^(1/2)+2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*d*(-c^2+d^2)^(1/2)*(-a^2+b^2)^(1/2)-EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*a*c*d-EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*a*c*(-c^2+d^2)^(1/2)-EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*b*c^2+2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*b*d^2+2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*b*d*(-c^2+d^2)^(1/2)-EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*c^2*(-a^2+b^2)^(1/2)+2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*d^2*(-a^2+b^2)^(1/2)+2*EllipticPi((((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2),(d+(-c^2+d^2)^(1/2))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b),1/2*2^(1/2)*((d+(-c^2+d^2)^(1/2))/(-c^2+d^2)^(1/2))^(1/2))*d*(-c^2+d^2)^(1/2)*(-a^2+b^2)^(1/2))*(g*sin(f*x+e))^(1/2)*sin(f*x+e)/(c+d*sin(f*x+e))^(1/2)*2^(1/2)*((-1+cos(f*x+e))*c/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2)*(((-c^2+d^2)^(1/2)*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-c)/(-c^2+d^2)^(1/2)/sin(f*x+e))^(1/2)*(((-c^2+d^2)^(1/2)*sin(f*x+e)+d*sin(f*x+e)-c*cos(f*x+e)+c)/(d+(-c^2+d^2)^(1/2))/sin(f*x+e))^(1/2)/(-1+cos(f*x+e))*a/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b)/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b)/(-a^2+b^2)^(1/2)","B"
48,1,269176,361,4.993000," ","int((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e),x)","\text{output too large to display}"," ",0,"result too large to display","C"
49,1,32723,183,1.059000," ","int((a+b*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
50,1,26871,368,0.866000," ","int(1/sin(f*x+e)/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
51,0,0,145,8.538000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))^p*(c-c*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)^{p} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))^p*(c-c*sin(f*x+e))^n,x)","F"